{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:T7P5Q4KMXLFVEOD6DRTAEOHY43","short_pith_number":"pith:T7P5Q4KM","canonical_record":{"source":{"id":"1509.02455","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2015-09-08T17:23:34Z","cross_cats_sorted":["math.AT","math.DS"],"title_canon_sha256":"7efcb7837b94f4fddcd99ed17c8633c73d7f4ae6de2bd4d93c4c11cbb15f4a9f","abstract_canon_sha256":"a8c4cd4d1fe51b6e3d8d5858fe037d0ea6f14c8a1ee1164d0c4fe955ece5581e"},"schema_version":"1.0"},"canonical_sha256":"9fdfd8714cbacb52387e1c660238f8e6e96a4f95fc20b91ebbec906cb1759b30","source":{"kind":"arxiv","id":"1509.02455","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.02455","created_at":"2026-05-18T00:41:53Z"},{"alias_kind":"arxiv_version","alias_value":"1509.02455v3","created_at":"2026-05-18T00:41:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.02455","created_at":"2026-05-18T00:41:53Z"},{"alias_kind":"pith_short_12","alias_value":"T7P5Q4KMXLFV","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_16","alias_value":"T7P5Q4KMXLFVEOD6","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_8","alias_value":"T7P5Q4KM","created_at":"2026-05-18T12:29:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:T7P5Q4KMXLFVEOD6DRTAEOHY43","target":"record","payload":{"canonical_record":{"source":{"id":"1509.02455","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2015-09-08T17:23:34Z","cross_cats_sorted":["math.AT","math.DS"],"title_canon_sha256":"7efcb7837b94f4fddcd99ed17c8633c73d7f4ae6de2bd4d93c4c11cbb15f4a9f","abstract_canon_sha256":"a8c4cd4d1fe51b6e3d8d5858fe037d0ea6f14c8a1ee1164d0c4fe955ece5581e"},"schema_version":"1.0"},"canonical_sha256":"9fdfd8714cbacb52387e1c660238f8e6e96a4f95fc20b91ebbec906cb1759b30","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:41:53.864843Z","signature_b64":"20hEZsuHupX1HzYnLmW4cIbjCCvmMG3o1ColKJ+8PLFMKoKddVroTLEhRZmn8mKWJM3i0zRYThoNYsOZkTFfAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9fdfd8714cbacb52387e1c660238f8e6e96a4f95fc20b91ebbec906cb1759b30","last_reissued_at":"2026-05-18T00:41:53.864096Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:41:53.864096Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1509.02455","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:41:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7TGGH0hm9BdliDWLgFNIxIM5E1syx8+fJBSolnyVXfkAUeREjv6EFDTW80CdHcCMtRClIHdXPhMIektNlGZvAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T20:57:15.016658Z"},"content_sha256":"e62351e6ba59b55f4320c425af44dc4a66dcad282ed01cefc2eeff7c98e350da","schema_version":"1.0","event_id":"sha256:e62351e6ba59b55f4320c425af44dc4a66dcad282ed01cefc2eeff7c98e350da"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:T7P5Q4KMXLFVEOD6DRTAEOHY43","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Local systems on the free loop space and finiteness of the Hofer-Zehnder capacity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT","math.DS"],"primary_cat":"math.SG","authors_text":"Alexandru Oancea, Peter Albers, Urs Frauenfelder","submitted_at":"2015-09-08T17:23:34Z","abstract_excerpt":"In this article we examine under which conditions symplectic homology with local coefficients of a unit disk bundle $D^*M$ vanishes. For instance this is the case if the Hurewicz map $\\pi_2(M)\\to H_2(M;\\mathbb{Z})$ is nonzero. As an application we prove finiteness of the $\\pi_1$-sensitive Hofer-Zehnder capacity of unit disk bundles in these cases. We also prove uniruledness for such cotangent bundles. Moreover, we find an obstruction to the existence of $H$-space structures on general topological spaces, formulated in terms of local systems."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.02455","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:41:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"o8T/YgpRVGhbjoTBcAUfBIQbUqRzBtbeM9L8MdH9m78wuvVcdoFKm/oIM2ncz6K856kVJmHXTfQ5mUkOiyKIBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T20:57:15.017008Z"},"content_sha256":"8fed97623fcdbe5801a36241680911c18e2c9e04067c0707af72fbb83c0d2ffd","schema_version":"1.0","event_id":"sha256:8fed97623fcdbe5801a36241680911c18e2c9e04067c0707af72fbb83c0d2ffd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/T7P5Q4KMXLFVEOD6DRTAEOHY43/bundle.json","state_url":"https://pith.science/pith/T7P5Q4KMXLFVEOD6DRTAEOHY43/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/T7P5Q4KMXLFVEOD6DRTAEOHY43/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-30T20:57:15Z","links":{"resolver":"https://pith.science/pith/T7P5Q4KMXLFVEOD6DRTAEOHY43","bundle":"https://pith.science/pith/T7P5Q4KMXLFVEOD6DRTAEOHY43/bundle.json","state":"https://pith.science/pith/T7P5Q4KMXLFVEOD6DRTAEOHY43/state.json","well_known_bundle":"https://pith.science/.well-known/pith/T7P5Q4KMXLFVEOD6DRTAEOHY43/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:T7P5Q4KMXLFVEOD6DRTAEOHY43","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"a8c4cd4d1fe51b6e3d8d5858fe037d0ea6f14c8a1ee1164d0c4fe955ece5581e","cross_cats_sorted":["math.AT","math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2015-09-08T17:23:34Z","title_canon_sha256":"7efcb7837b94f4fddcd99ed17c8633c73d7f4ae6de2bd4d93c4c11cbb15f4a9f"},"schema_version":"1.0","source":{"id":"1509.02455","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.02455","created_at":"2026-05-18T00:41:53Z"},{"alias_kind":"arxiv_version","alias_value":"1509.02455v3","created_at":"2026-05-18T00:41:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.02455","created_at":"2026-05-18T00:41:53Z"},{"alias_kind":"pith_short_12","alias_value":"T7P5Q4KMXLFV","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_16","alias_value":"T7P5Q4KMXLFVEOD6","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_8","alias_value":"T7P5Q4KM","created_at":"2026-05-18T12:29:42Z"}],"graph_snapshots":[{"event_id":"sha256:8fed97623fcdbe5801a36241680911c18e2c9e04067c0707af72fbb83c0d2ffd","target":"graph","created_at":"2026-05-18T00:41:53Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"In this article we examine under which conditions symplectic homology with local coefficients of a unit disk bundle $D^*M$ vanishes. For instance this is the case if the Hurewicz map $\\pi_2(M)\\to H_2(M;\\mathbb{Z})$ is nonzero. As an application we prove finiteness of the $\\pi_1$-sensitive Hofer-Zehnder capacity of unit disk bundles in these cases. We also prove uniruledness for such cotangent bundles. Moreover, we find an obstruction to the existence of $H$-space structures on general topological spaces, formulated in terms of local systems.","authors_text":"Alexandru Oancea, Peter Albers, Urs Frauenfelder","cross_cats":["math.AT","math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2015-09-08T17:23:34Z","title":"Local systems on the free loop space and finiteness of the Hofer-Zehnder capacity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.02455","kind":"arxiv","version":3},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:e62351e6ba59b55f4320c425af44dc4a66dcad282ed01cefc2eeff7c98e350da","target":"record","created_at":"2026-05-18T00:41:53Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"a8c4cd4d1fe51b6e3d8d5858fe037d0ea6f14c8a1ee1164d0c4fe955ece5581e","cross_cats_sorted":["math.AT","math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2015-09-08T17:23:34Z","title_canon_sha256":"7efcb7837b94f4fddcd99ed17c8633c73d7f4ae6de2bd4d93c4c11cbb15f4a9f"},"schema_version":"1.0","source":{"id":"1509.02455","kind":"arxiv","version":3}},"canonical_sha256":"9fdfd8714cbacb52387e1c660238f8e6e96a4f95fc20b91ebbec906cb1759b30","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9fdfd8714cbacb52387e1c660238f8e6e96a4f95fc20b91ebbec906cb1759b30","first_computed_at":"2026-05-18T00:41:53.864096Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:41:53.864096Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"20hEZsuHupX1HzYnLmW4cIbjCCvmMG3o1ColKJ+8PLFMKoKddVroTLEhRZmn8mKWJM3i0zRYThoNYsOZkTFfAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:41:53.864843Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.02455","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e62351e6ba59b55f4320c425af44dc4a66dcad282ed01cefc2eeff7c98e350da","sha256:8fed97623fcdbe5801a36241680911c18e2c9e04067c0707af72fbb83c0d2ffd"],"state_sha256":"c13531465fb47bb29d161bcb7e2e8921661e3e49867c24e69e39ab6f9907f7c5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gaRfOiR6t8p20iYOkTGsraAKSIkzwoC8sElMT9MFC0cCq9YYCZarT+v/VIaBIcC5hHP2qf18hACv9b9hg6bLAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T20:57:15.019081Z","bundle_sha256":"cf22752d87c1c24c4466649f6fa6a21eeaf7d52746efe9386e2fb7b5eef8db2e"}}